HOW   TO    MAKE 
LOW-PRESSURE 

TRANSFORMERS 


'RICE  40  CENTS 


How   to  Make  Low-Pressure 
Transformers 


THIRD  EDITION 


WITH    ADDITIONS       , 


BY 


PROF.  F.  E.  AUSTIN,  HANOVER,  N.  H. 

Ik  A 

AUTHOR  OF 

"EXAMPLES  IN  ALTERNATING- CURRENTS" 
"EXAMPLES  IN  MAGNETISM" 

"DIRECTIONS   FOR   DESIGNING,   MAKING  AND  OPERATING 
HIGH-PRESSURE  TRANSFORMERS." 


Srond  Edition  Copyright  1916  by  F.  E.  Austin. 
Third  Edition  Copyright  1916  by  F.  K  Austin. 


HANOVER,  N.   H 


PREFACE  TO  SECOND  EDITION. 

The  hearty  reception  of  the  first  edition  of  this  small  book  has  been 
very  gratifying  to  the  author  who  takes  opportunity  to  answer,  in  the 
second  edition,  in  the  form  of  additional  subject  matter,  a  number  of 
questions  pertaining  to  fundamental  principles,  addressed  to  him  by  those 
interested  in  transformer  construction;  hoping  by  this  method  to  aid 
many  who  desire  to  depart  somewhat  from  the  printed  specifications  and 
construct  with  similar  material,  transformers  for  a  variety  of  application. 

Pertaining  to  design  it  is  probable  there  is  no  form  of  core  that  will 
•effect  so  high  operative  efficiency  as  the  form  of  discs  recommended. 

The  numerous  transformers  made  by  amateurs  according  to  the 
specifications  and  submitted  to  the  writer  for  test,  have  all  shown  won- 
derfully high  efficiencies  for  so  small  devices. 

PREFACE  TO  THE  THIRD  EDITION. 

The  increasing  popularity  of  "How  to  Make  Low-Pressure  Trans- 
formers", has  rendered  a  third  edition  necessary.  The  wide  spread  sale 
of  the  book  has  been  a  pleasing  feature.  Copies  have  been  sold  in  Alaska, 
the  Panama  Canal  Zone,  the  Philippines,  Norway,  Italy,  and  throughout 
the  United  States,  Canada  and  England.  While  in  the  third  edition 
the  book  has  been  greatly  enlarged,  the  price  has  not  been  increased. 

In  this  edition  a  new  and  very  simple  form  of  core  construction 
is  described  on  page  14. 

Due  to  the  desire  of  many  amateurs  to  make  a  small  transformer 
without  the  use  of  discs  for  a  core,  a  very  simple  type  is  described  in  this 
edition,  beginning  on  page  16.  A  ve/y  novel  utilization  of  discarded 
"tin  cans"  as  transformer  cores  is  also  explained  on  page  20;  being  a  lesson 
in  the  conservation  of  resources;:  scrA-the  making  of  one  transformer  where 
none  existed  before.  .'  • 


Introductory 


Being  constantly  in  receipt  of  inquiries  regarding  the  design,  construc- 
tion, and  operation  of  small  transformers  for  exparimental  purposes,  the  fol- 
lowing instructions  have  been  put  into  the  present  form,  to  enable  anyone  to 
build  a  small  transformer,  at  a  small  cost,  without  the  use  of  .expensive 
tools  or  machinery,  that  may  be  connected  with  any  house  circuit  where 
the  pressure  is  110  volts  or  less,  and  the  frequency  about  60  cycles. 

The  particular  shape  adopted,  while  excellent  as  regards  ease  of  con- 
struction, is  also  conducive  to  high  operative  efficiency;  meaning  that  the 
meter  bill  will  be  a  minimum.  The  high  efficiency  is  due  to  the  high 
permeability  of  the  iron  used  and  also  to  the  fact  there  are  no  "magnetic 
joints"  in  the  core  of  the  transformer. 

Many  of  these  transformers  have  been  made  by  students  in  our  lab- 
oratories, with  a  variety  of  windings  on  the  same  size  and  shape  of  core,  to 
produce  a  variety  of  pressures  and  out-puts. 

The  transformer  here  described,  is  a  "step-down"  transformer,  to  re- 
duce the  pressure  from  110  volts,  to  about  8  volts  as  a  minimum,  for  ex- 
perimental purposes;  such  as  operating  low  pressure  tungsten  lamps; 
ringing  bells,  operating  small  direct-current  series  motors,  used  with  fans 
or  small  electric  cars;  operating  sparking  devices  for  gasolene  engines; 
operating  small  arc-lights,  and  for  a  variety  of  other  uses. 

While  the  primary  winding  of  this  transformer  is  the  same,  regardless 
of  the  secondary  or  step-down  pressure  when  connected  with  the  110  volt 
mains  at  60  cycles,  the  secondary  pressure  may  be  varied  at  will  by  vary- 
ing the  number  of  turns  in  its  secondary  windings,  when  constructing  the 
transformer. 

The  amateur  is  advised  not  to  make  a  "step-up"  transformer  of  the 
material  here  described, 'since  this  type  of  transformer  is  not  designed  for 
high  pressures  and  the  result  of  applying  high  pressures  might  be  disastrous 
for  the  transformer,  if  not  resulting  in  injury  to  the  house  wiring  and  ex- 
rimenter. 

If  it  is  desired  to  build  a  high-pressure  transformer  for  wireless 
experiments,  information  may  be  obtained  from  the  book  entitled  "Direc- 
tions for  Making  and  Operating  a  High  Pressure  Transformer" 
by  Prof  F.  E.  Austin,  mentioned  in  the  last  part  of  this  book. 

While  the'  transformer  to  be  described  in  the  following  outline,  may 
be  rated  as  a  100  watt  transformer,  when  operating  at  its  maximum  effi- 
ciency, it  will  transform  much  more  power  without  over  heating.  As  may 
be  seen  from  the  efficiency  curve,  figure  6,  page  12,  which  was  drawn  from 

345211 


floir  to  Mdl'f  ficw-Preaffure  Transformers. 


actual  experiment  :J  dut-i  obtained  from  .osting  one  of  the  transformers 
made  by  students  in  our  laboratories,  the  output  may  be  400  watts;  and 
this  without  serious  heating,  if  not  too  long  continued.  However  the 
efficiency  at  this  output  is  only  slightly  over  70%;  while  at  100  watts 
output  the  efficiency  is  over  90  per  cent;  a  high  efficiency  for  a  small 
device. 

The  power  input  to  the  transformer  is  always  greater  than  the  power 
output  because  of  the  various  losses  within  it.  The  power  efficiency  of  the 
transformer  at  any  output  is  always  the  ratio  of  the  output,  in  watts, 
to  the  input,  in  watts,  when  the  "load"  connected  with  the  secondary  is 
"non-inductive";  that  is  not  consisting  of  coils  or  motors,  but  of  lamps, 
(incandescent)  or  a  liquid  rheostat. 

The  core  of  the  transformer  consists  of  50  annular  rings  or  washers 
9  inches  diameter  over  all  with  a  6  inch  diameter  central  hole,  punched  from 
thin  plates  of  so  called  "electrical-steel"  about  .015  of  an  inch  in  thickness. 

The  total  thickness  of  the  50  rings,  unvarnished,  when  tightly  clamped 
together  is  about  .744  inch.  Since  the  width  of  the  annular  portion  is 
1  5  inch,  the  cross  sectional  area  of  the  iron  in  the  core  is 

744      =    1500     x      744  1.5   X  7.44    =  1.11  inch 

1000  1000  1000  10  (approx.) 

The  total  weight  of  the  50  rings  is  about  t>  pounds  and  11  ounces. 

It  should  be  noted  that  the  useful  power  output  of  this  transformer 
is  over  5  horse-power. 


Directions 


1.  Carefully  remove  all  sharp  edges  and  burrs  from  the  edges  of  the 
rings  by  means  of  a  fine  half-round  file  or  sand  paper. 

2.  Carefully  count  the  rings,  weigh  them  and  measure  their  thickness 
and  width. 

3.  Coat  both  sides  and  edges  of  each  punching  or  disc  with  shellac 
varnish  or  some  other  good  insulating  varnish.     Shellac  varnish  seems  to 
give  as  good  results  as  any  varnish  and  can  be  easily  made  by  any  one;  be- 
ing simply  gum-shellac  dissolved  in  sufficient  denatured  alcohol  to  give  the 
proper  consistency  to  spread  easily,  with  a  brush.     If  too  thick,  it  may  be 
thinned  by  adding  more  alcohol.     Do  not  use  the  powdered  shellac  if  the 
orange  flake  shellac  can  be  obtained. 

4.  As  soon  as  each  disc  has  been  carefully  varnished,  hang  it  on  a  hor- 
izontal stick,  to  become  thoroughly  dried.      This  may  require  five  to  ten 


How  to  Make  Low- Pressure  Transformers.  5 

hours  in  a  warm  room.  The  supporting  stick  may  be  long  enough  and  of 
sufficient  strength  to  support  all  50  discs.  Do  not  allow  the  varnished  discs 
to  come  into  contact  with  one  another  before  they  are  dry.  See  figure  1, 
a.  page  5. 

5.  Cut  carefully  from  thin  brown  or  white  wrapping  paper,  50  annular 
rings  having  the  same  size  as  the  steel  punchings,  to  be  used  to  insulate 
each  punching  from  its  neighbor  when  assembled.  A  large  sheet  of  the  wrap- 
ping paper  may  be  folded  into  a  square  somewhat  larger  than  a  punching 
then  with  a  punching  as  a  pattern,  using  a  small  sharp  pen  knife,  a  number 
of  paper  rings  may  be  cut  at  one  operation.     These  may  be  cut  while 
the  varnished  discs  are  drying. 

6.  After  the  varnished  discs  are  well  dried,  they  should  be  assembled 
by  placing  one  disc  on  a  level  board  between  three  or  more  wooden  pegs 
which  are  inserted  in  holes  inxthe  board  so  the  pegs  are  perpendicular  to  the 
surface  of  the  board,  and  at  such  distance  from  each  other  as  to  allow  the 
disc  to  just  touch  them  when  placed  between  them.     See  figure  l,b.     Ap- 
ply a  thin  coat  of  varnish  to  the  upper  surface  of  the  first  disc  and  immed- 
iately place  a  paper  ring  on  the  newly  varnished  disc.     Place  another  steel 
disc  on  top  of  the  paper  ring  and  apply  a  thin  coating  of  varnish  to  its 
upper   surface,    upon   which   place   another   paper   ring.     Continue    this 
process  until  all  the  steel  discs  have  been  used. 

7.  After  the  assembled  pile  of  discs  have  been  allowed  to  dry  for 
several  hours  carefully  remove  the  pile  from  the  board  and  clamp  together  in 
a  vice,  and  in  two  or  more  places  by  wooden  hand  screws.  The  vise  is  not 
necessary  but  serves  to  hold  the  assembled  discs  firmly  in  position  for  the 
next  operation. 


FIG.  1. 


How  to  Make  Low- Pressure  Transformers. 


.  I H  mBi    .         Ss I  '     ••:...:...-. 

FIG.  2.  FIG.  3. 

8.  Begin  to  wind    ordinary    electricans'  sticky  tape,  about  f  inch 
wide,  around  the  assembled  discs  between  two  of  the  attached  clamps, 
which  should  be  placed  about  two  inches  apart.     Lap  the  edges  of  tape 
about  £  inch. 

After  the  tape  has  been  wound  tightly  over  this  space,  remove  the 
clamp  up  to  which  the  tape  has  been  wound,  and  place  it  so  as  to  again 
clamp  the  discs  at  a  distance  of  about  two  inches  from  the  point  where  the 
winding  of  the  tape  was  stopped.  Continue  to  tape  over  this  space  of  two 
inches,  up  to  the  clamp.  Proceed  in  this  manner  until  the  whole  transfor- 
mer core  has  been  tightly  taped.  See  figure  1,  page  5. 

If  the  adhesive  tape  is  lapped  |  inch  on  the  outer  circumference  of 
the  core,  it  will  of  course  lap  more  in  passing  around  the  inner  circumference. 
Two  layers  of  tape  will  be  advisable. 

9.  Next  wind  on  the  core,  over  the  tape,  as  many  turns  as  possible 
in  one  layer,  of  No.  22  double  cotton  covered  copper  magnet  wire,  so  as  to 
cover  one-half  of  the  core.     To  facilitate  the  process  of  winding,  this  wire 
should  first  be  wound  onto  a  spool  that  is  small  enough  to  be  easily  passed 
through  the  circular  hole  of  the  transformer  core. 

Fasten  one  end  of  the  wire  by  clamping  it,  or  by  any  method  that  wrill 
not  injure  it  or  the  tape  on  the  core,  and  passing  the  spool  of  wire  through 
the  central  hole,  wind  the  wire  so  the  successive  turns  as  they  pass  through 
the  central  hole,  lie  close  to  each  other.  The  proper  action  of  the  completed 
transformer  depends  largely  on  the  care  observed  in  winding  the  coils. 

The  turns  of  wire  as  they  pass  around  the  outer  circumference  will  be 
slightly  separated  from  each  other  and  this  distance  should  be  the  same  be- 
tween  each  turn  if  possible. 

Each  terminal  of  the  primary  should  be  properly  tagged  to  show  the 
number  of  turns  and  whether  the  terminal  is  an  inside  one  or  an  outside  one. 
See  figure  2,  page  6. 


How  to  Make  Low- Pressure  Transformers.  7 

The  four  terminals  of  the  two  primary  sections  are  shown  at  P,  P'; 
figure  2,  page  6  the  other  eight  terminals  being  those  of  the  secondary 
coils. 

The  second  half  of  the  core  should  be  wound  with  the  same  kind  of 
wire,  observing  the  same  precautions  as  with  the  first  half,  and  should  be 
wound  in  the  same  direction. 

The  two  coils  should  consist  of  about  484  turns,  total,  and  constitute 
the  ''primary"  of  the  transformer.  See  figure  2,  P.  P',  page  6. 

There  will  be  four  free  ends  of  wire,  and  when  two  adjacent  ends  are 
connected  together  and  the  two  remaining  free  ends  connected  with  a 
cricuit,  the  two  coils  will  act  together',  or  not  in  "opposition." 

10.  Apply  two  coats  of  varnish  to  the  wire  of  the  primary  coils, 
allowing  the  first  coat  to  dry  during  several  hours  before  applying  the 
>«'<•< >nd  coat. 

11.  Carefully  count  the  number  of  turns  of  wire  on  the  primary, 
and  record  the  number. 

12.  Cut  two  annular  rings  from  thick  card  board,  each  ring  having  an 
over  all  diameter  about  £  inch  greater  than  the  overall  diameter  of  the 
transformer  as   already   constructed;   that  is,   inclusive  of  the  primary 
windings. 

The  diameter  of  the  central  hole  in  each  cardboard  disc  should  be 
about  £  inch  less  than  the  diameter  of  the  central  hole  in  the  transformer 
a.<  wound. 

13.  These  cardboard  discs  should  be  carefully  varnished  with  at 
least  two  coats  of  shellac  varnish  and  very  thoroughly  dried.     Certain 
kinds  of  cardboard  may  need  three  or  more  coats. 


FIG.  4. 


>  Hoic  to  Make  Loiv- Pressure  Tram/onm 

14.  Cut  strips  from  the  same  card-board  material  from  which  the 
cardboard  discs  are  made,  which  have  a  width  equal  to  the  thickness  of  the 
transformer  inclusive  of  the  primary  winding,  and  long  enough  to  encircle 
the  inner  circumference  of  the  transformer  and  also  the  outer  circumference. 
Two  strips  may  be  used  for  the  outer  circumference  if  one  strip  cannot 
be  obtained  of  sufficient  length.     These  strips  should  be  varnished  like 
the  card  board  discs. 

15.  Carefully  wind  each  terminal  P.  P',  figure  2,  page  G,  of  the  pri- 
mary coil  with  insulating  tape  to  insulate  the  terminals  as  they  pass  out 
through    the    cardboard    insulation  that  is  placed  between  the  pri: 
and  the  secondary.     Considerable  care  regarding  this  feature  should  be 
taken,  that  no  short-circuit  or  ground  can  take  place  between  the  primary 
and  secondary  windings. 

16.  Place  one  of  the  cardboard  discs  on  one  side  of  the  transf 
against  the  primary  wires,  and  the  other  disc  on  the  opposite  side.     Fi 
varnished  cardboard  strips  around  the  edges  of  the  transformer   bei 
the  circumferences  of  the  two   cardboard  discs  and  hold  all  in  po- 
temporarily  by  means  of  string.     The  primary  is  now  completely  co1 
with  varnished  cardboard  which  serves  to  insulate  the  prii 
secondary  windings. 

17.  Next    wind    carefully    over    the  cardboard    covering,    N 
double  cotton  covered  copper  magnet  wire  in  four  sections.     The  first  two 
sections  occupy  \  of  the  transformer  per  section;  or  \  of  the  transformer 
for  both  sections.     Another  section  should  occupy  f  of  the  unwound  half 
or  $  of  the  whole  transformer,  while  the  last  section  occupies  the  reni  i 

5  of  £,  or  5  of  the  whole  transformer. 

The  secondary  is  wound  in  one  layer,  with  the  turns  on 
circumference  lying  close  together  and  evenly  spaced  on 
cumference,  and  is  to  be  wound  always  continuously  in  th< 
as  was  the  primary.     That  is  in  such  manner  that   if   all  th 
free  ends  were  connected  together  it  would  form  one  continuous  wincing. 
Figure  4,  page  7,  will  illustrate. 

18.  The  secondary  winding  should  be  given  two  or  three  coats  of 
varnish;  allowing  each  coat  to  dry  thoroughly  before  applying  the  succeed- 
ing coat . 

19.  For  convenience  the  transformer  may  be  mounted  on  a  board 
base  about  12^  or  13  inches  square  and  about  1  inch  thick,  and  the  var- 
ious terminals  brought  out  to  binding  posts  as  indicated  in  figure  3.  pane 
6,  which  shows  a  finished  transformer,  having  12  binding  posts;  one  for 
each  primary  and  each  secondary  terminal. 

In  the  figure  the  four  posts  below  the  white  line  are  the  four  primary 
connections  and  the  other  eight  posts  are  the  secondary  connections. 

The  following  tabulated  data  applies  to  a  transformer  made  in  our 
laboratory  according  to  directions  given  in  this  book. 


How  to  Make  Low-Pressure  Transformers. 


"     9 


Core : 


Primary : 


Secondary 


TRANSFORMER. 

50  annular  discs  of  "electrical  steel". 

Total  weight  of  50  discs,  107  ozs.  (6  Ibg.  11  ozs.  ) 

Weight  of  each  disc,  2.14  ozs. 

Total  thickness  of  50  discs  not  varnished,  0.744  inch. 


Average  thickness  of  each  disc,  -  inch  . 

.  1000 

Outside  diameter  of  disc,  9  inci 
Diameter  of  central  hole,  6  inches. 
Width  of  annular  portion,  1  \  inch. 
Cross  sectional  area  1.11  square  inch. 

485  turns,  of  No.  22  D.  C.  C.  copper  magnet  wire. 

Wound  in  two  sections. 

Total  resistance  of  primary  wire,  at  70°  F  (or  2l°C)  3.8  ohm. 

Total  length  of  primary  wire,  204  feet. 

Total  weight  of  primary  wire,  7  ozs. 

2.S7  turns,  of  No.  16  D.  C.  C.  copper  magnet  wire. 

Wound  in  four  sections. 

Total  resistance  of  secondary  at  70°F  (or  21°C)  is  0.63  ohm. 

Total  length  of  secondary  137  feet. 

Tot  al  weight  of  secondary  24  ozs.  or  1  Ib.  8  oz. 


FIG.  5. 


10 


How  to  Make  Low-Pressure  Transformers. 


The  reason  for  winding  the  secondary  in  unequal  sections,  is  to  obtain 
a  wide  variation  in  pressure. 

Without  direct  reference  to  any  particular  transformer  that,  has  been 
built,  suppose  diagram  figure  4,  page  7  denotes  a  transformer  with  a  secondary 
having  four  sections,  two  of  which,  1  and  2  are  equal  to  each  other,  and  the 
pressure  of  each  section  is  |  the  total  secondary  pressure. 

Let  it  be  assumed  the  total  no-load  secondary  pressure  is  64  volts; 
that  is  with  all  the  sections  connected  together  in  series  so  that  their  pres- 
sures are  all  added  together. 

The  sum  of  the  pressures  of  the  two  sections  having  the  same  number 
of  turns  will  be  32  volts  when  they  are  connected  together  in  series;  SP<> 
between  a  and  d,  figure  4,  page  7. 

Now  suppose  sections  1  and  2  are  connected  together  in  opposition,  by 
•changing  their  terminal  connections;  that  is  terminal  d  be  connected  with 
terminal  b;  then  the  pressure  between  a  and  c  will  be  zero.  Two  equal 
pressures,  numerically,  being  opposed  to  each  other. 

Next  suppose  terminals  of  coils  3  and  4  are  connected  as  at  f  and  g; 
then  the  pressure  between  e  and  h  will  be  8  +  24  =32  volts.  There- 
fore the  two  sections  formed  by  coils  1  and  2  in  series,  and  coils  3  and 
4  in  series,  could  be  connected  together  in  parallel,  for  heavier  current  out- 
put. Both  sections  thus  formed  could  supply  twice  as  much  current  to  a 
load  as  could  one  section  alone.  Coil  4  having  three  times  as  many 
turns  as  coil  3. 

Figure  4  indicates  the  pressure  obtainable  from  each  of  the  four  coils; 
namely  8,  16  and  24  volts,  together  with  two  other  possible  pressures. 
.32  and  64,  resulting  from  properly  connecting  the  coils  together. 

A  large  number  of  different  pressures  may  be  obtained  by  connecting 
certain  coils  in  opposition. 

Instead  of  connecting  3  and  4  properly  in  series  to  produce  32  volts, 
suppose  the  two  coils  are  connected  together  in  opposition,  by  reversing 
their  terminal  connections.  Then  the  pressure  between  the  free  ends 
will  be  24-8  or  16  volts. 

The  following  pressures  as  tabulated,  show  some  possibilities. 


Connections  of  Coils 

Resulting  Pressure 

3  or  2-3  or  1-3 
1  or  2  or  4  -  3 
4  or  2  +  3  or  1  +  3 
1   +  2  or  3  +  4 
4  +  1  or  4  +  2 
4  +  3  +  2  or  4  +  3  +  1 
4  +  1+2 

16  -      8  or  8  volts 
24  -      8  or  16     " 
16  +     8  or  24     " 

-..SiJfe-  " 

24  +  16  or  40     " 
24  +     8  +  16  or  48     " 
24  +  16  +  16  or  56     " 

How  to  Make  Low- Pressure  Transformers.  -    11 

The  negative  or  -  sign  denotes  that  the  coils  are  connected  together 
in  opposition;  while  the  positive  or  +  sign  denotes  that  the  coils  are  so  con- 
nected that  their  pressures  are  added  together. 

Figure  5,  page  9,  gives  some  idea  of  the  application  of  the  transformer 
as  a  "booster",  or  auto- transformer,  if  part  of  the  primary  is  employed. 
The  arrangement  indicated  in  figure  5  is  such  that  the  pressure  applied 
may  be  boosted,  in  steps,  from  110  to  174  volts.  In  order  not  to  over  heat 
the  transformer,  no  greater  current  should  be  taken  from  the  device  when 
used  as  booster,  than  the  primary  winding  is  designed  for.  Other  pres- 
sures than  those  indicated,  may  be  obtained;  as  between  A  D,  is  48  volts; 
between  A  E,  64  volts.  Also  if  secondary  coil  4,  figure  5,  is  connected  in 
opposition  to  the  primary  pressure,  then  about  110-24  =  68  volts  may  be 
obtained,  the  transformer  acting  as  a  "crusher",  or  negative  booster. 

The  primary  pressure,  less  any  of  the  other  coil  pressures,  will  give 
other  possible  values. 

When  wound  according  to  the  instructions  given  here,  the  input  to  the 
transformer  at  no  load  secondary,  when  primary  is  connected  across  ser- 
vice mains  having  a  pressure  of  110  volts  at  60  cycles,  is  about  11  watts. 

If  the  cost  of  electric  power  is  15  cts  per  kilo-watt  hour,  (1000  watt- 
hours)  the  cost  per  day  of  24  hours  of  having  the  unloaded  transformer 
connected  with  the  mains,  would  be 

11   X  24  X  15 

=  3.9  cents;  say  four  cents. 

1000 

This  is  about  \  cent  per  hour. 

.    According  to  the  curve  figure  6,  page  12,  when  operating  a  load  of  90 
watts  the  input  is  100  watts;  and  the  cost  per  hour  will  be: — 

100   X   1   X  15 

: =     1.5  cent. 

1000 

Compared  with  the  expense  of  batteries  to  furnish  the  same  amount  of 
power,  the  expense  is  small. 

The  upper  curve  of  figure  6,  page  12,  shows  the  efficiency  of  one  of 
these  transformers  under  various  conditions  of  output. 

The  cost  per-watt-hour  of  output  is  greater  when  the  transformer  'out- 
put is  400  watts  than  when  it  is  90  watts.  The  cost  per-watt-hour  is  the 
same  when  the  output  is  400  watts  as  when  it  is  only  46  watts,  as  indicated 
by  the  dotted  line. 

At  any  output  below  44  watts,  the  cost  per-watt-hour  increases  very 
rapidly,  since  the  efficiency  decreases  very  rapidly. 

The  cost  per-watt-hour  is  a  minimum,  when  the  efficiency  is  a  maxi- 
mum. 


12  •  How  to  Make  Low- Pressure  Transformer*. 

The  lower  curve  in  figure  6,  page  12,  shows  what  is  called  the  "regu- 
lation" of  the  transformer;  which  is  the  ratio  of  the  difference  between  the 
no-load  secondary  terminal  pressure  and  the  full-load  secondary  terminial 
pressure,  to  the  full  load  secondary  terminal  pressure,  when  the  load  connected 
with  the  secondary  is  non-inductive,  such  as  incandescent  lights.  The 
primary  applied  pressure  must  be  kept  constant  while  finding  the  regulation 

. 


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How  to  Make  Low- Pressure  Transformers.  13 

REGULATION. 

If  E  denotes  the  no-load  secondary  terminial  pressure,  in  volts, 
and  EI  denotes  the  full-load  secondary  terminal  pressure,  in  volts; 

E  -  EI 
then,  regulation    =  - 

EI 

when  the  applied  primary  pressure  is  maintained  constant  and  the  load 
on  secondary  is  non-inductive. 

The  middle  curve  in  figure  6,  page  12,  shows  the  drop  in  the  secondary 
terminal  pressure  as  the  load  output  increases. 

At  no  load  the  secondary  terminal  pressure  was  64  volts,  with  all  se- 
condary coils  connected  together  in  series  and  110  volts  60  cycles  applied 
to  primary  terminals. 

At  100  watts  output  the  secondary  terminal  pressure  fell  to  about  00 
volts;  while  at  400  watts  output  it  fell  to  about  47  volts.  The  pressure  ap- 
plied to  primary  was  kept  constant  at  110  volts. 

The  secondary  of  this  transformer  may  be  used  as  a  "choke-coil"  for 
currents  up  to  about  10  amperes.  By  tapping  in  at  different  secondary 
binding-posts,  various  "choking"  effects  may  be  obtained.  The  primary 
of  the  transformer  may  also  be  used  as  a  choke  coil,  but  for  very  much  smal- 
ler values  of  current;  about  2  or  3  amperes. 

RECAPITULATION. 

The  design  and  construction  of  the  transformer  just  described,  leads 
to  the  consideration  of  certain  fundamental  principles  it  is  well  to  have 
in  mind,  if  it  is  desired  to  vary  the  windings  of  the  secondary  to  meet  a 
variety  of  applications. 

Consulting  page  9  it  will  be  observed   that  the  primary  winding 
consists  of  485  turns.     If  the  pressure  applied  to  the  terminals  of  the 
primary  is  110  volts,  the  pressure  per  turn  of  primary  winding  is 
110 

-   =   0.22  volts.     One    turn    of    secondary    winding    will    have    very 
485 

nearly  the  same  pressure.  So  that  if  a  secondary  pressure  of  55  volts 
is  desired,  one  half  the  number  of  primary  turns  (that  is  243)  should 
be  wound  on  the  secondary.  If  one  fourth  the  number  of  primary  turns 
are  wound  on  for  the  secondary,  then  the  secondary  pressure  will  be 
110 

some  less  than or  about  27  volts. 

4 


11 


How  to  Make  Low-Pressure  Transformers. 


Considering  the  matter  from  another  standpoint,  it  will  be  neces- 
sary to  wind  on  about  4.5  turns  in  order  to  obtain  a  secondary  pressure 
of  one  volt.  All  of  the  foregoing  considerations  are  based  on  a  frequency 
of  60  cycles  per  second. 


SPECIAL  CORE  CONSTRUCTION. 

A  special  type  'of  core  may  be  constructed  from  the  ordinary  stove- 
pipe iron  obtainable  at  any  hardware  store,  as  follows:  First  construct 
a  form  on  which  to  build  up  the  core,  by  fastening  a  circular  wooden  disc, 
6  inches  in  diameter  and  f  inch  (or  even  £  inch)  thick  to  a  larger  board 
as  illustrated  by  D  in  figure  7. 

The  stove-pipe  iron  should  be  cut  from  the  large  sheets,  in  strips 
|  inch  wide,  carefully  varnished  all  over  with  shellac  varnish  and  wound 
over  the  form  in  a  spiral  as  shown  in  figure  8,  so  that  the  finished  core 
will  be  wound  to  a  depth  of  1^  inch.  In  other  words  the  cross  section 
of  this  core  is  to  be  the  same  as  the  cross  section  of  the  core  made  of  the 
circular  discs,  and  its  weight  will  also  be  the  same.  That  is,  the  amount 
of  stove-pipe  iron  required  will  be  about  6  Ibs.  and  11  oz.  Pieces  of  string 
or  tape  T  and  T'  figures  7  and  8,  may  be  laid  on  the  form  before  the  strips 
are  wound  on,  and  used  to  hold  the  wound  core  together  until  it  can  be 
covered  with  tape  as  directed  on  page  6,  section  8.  The  winding  of  the 
primary  and  of  the  secondary  will  be  exactly  the  same  with  this  spiral 
form  of  core  as  with  the  discs.  This  form  of  core  will  enable  many  to 
construct  transformers  of  \  horse-power  output,  who  find  it  inconvenient 
and  expensive  to  obtain  the  proper  discs. 


Fig.  7. 


Fig.  8 


How  to  Make  Low-Pressure  Transformers.  15 

A  TRANSFORMER  FOR  220  VOLTS  60  CYCLES. 

By  using  twice  as  many  discs  as  specified  on  page  9,  or  iron  strip  twice 
as  wide  as  out-lined  on  page  14,  and  using  the  same  size  of  primary  and 
and  same  number  of  turns  as  specified  on  page  9,  a  transformer  may  be 
made,  adapted  for  220  volts,  60  cycles  primary  pressure.  If  the  primary 
winding  is  wound  in  two  equal  sections  (same  number  of  turns  in  each 
section)  each  section  may  be  connected  with  110  volts  60  cycles;  or  the 
two  equal  sections  may  be  properly  connected  together  in  parallel  and  the 
arrangement  connected  with  110  volt  60  cycle  mams,  giving  a  transformer 
with  a  continuous  full  load  output  of  over  one  horse  power.  If  the  trans- 
former is  connected  with  220  volt  60  cycle  mains,  the  two  sections  of  pri- 
mary winding  should  be  connected  together  in  series;  in  which  case  the 
continuous  full  load  working  output  will  be  some  over  one  horse  power. 
Xo.  10  double  covered  cotton  wound  magnet  wire  should  be  used  on  such 
a  transformer  for  a  secondary  winding;  being  wound  as  closely  as  possible 
in  one  layer. 

The  same  reasoning  as  regards  pressures  applies  in  the  case  of  a 
220  volt  transformer,  as  given  above  for  a  110  volt  transformer.  With  the 
same  number  of  secondary  turns  on  the  220  volt,  as  on  the  110  volt  trans- 
former, and  with  220  volt  60  cycle  primary  pressure,  the  secondary  pres- 
sure will  be  about  twice  as  great  as  on  the  1 10  volt  transformer. 

Great  care  should  be  exercised  in  winding  the  insulating  tape  around 
the  iron  core.  If  a  cheap  grade  of  electrician's  sticky  tape  is  used  it  will 
be  advisable  to  wind  two  layers,  one  over  the  other. 

Instead  of  using  this  class  of  insulating  tape,  ordinary  cloth  tape 
|  inch  wide  may  be  wound  over  the  iron  core,  making  a  |  inch  lap  along 
the  edges  of  the  windings,  carefully  coating  the  finished  winding  with 
shellac  varnish.  After  the  varnish  is  thoroughly  dry,  wind  another  layer 
of  the  cloth  tape  over  the  first  and  shellac  this  layer. 

In  winding  the  primary  wire  on  the  taped  core,  do  not  pull  the  wire 
too  tightly  in  winding  over  the  corners  of  the  core.  If  wound  too  tightly 
the  sharp  edges  of  the  discs  may  cut  through  the  insulation,  causing 
"shorts";  that  is  short  circuits. 


16 


How  to  Make  Low-Pressure  Transformers 


SPECIAL  TYPE  OF  CONSTRUCTION. 


The  following  working  directions  for  making  a  different  form  of  low- 
pressure  transformers  may  appeal  to  those  who  desire  to  experiment  with 
different  coil  windings;  the  arrangement  being  such  as  to  allow  the  forms 
or  spools,  on  which  the  coils  are  wound,  to  be  quickly  and  easily  removed 
from  the  core,  and  others  substituted,  or  the  same  rewound  by  beinu 
readily  slipped  on  to  a  specially  designed  winding  device,  shown  in  figure 
15,  page  18. 

No  lengthy  explanation  is  necessary,  because  of  the  insertion  of  the 
working  diagram  on  pages  16,  17,  18  and  19,  with  the  dimensions  clearly 
indicated  thereon. 

The  core  consists  of  124  pieces  of  transformer  steel  each  6|  inches  long 
by  1  inch  wide,  and  124  pieces  of  the  same  material  3|  inches  long  by  1 
inch  wide;  the  material  being  about  .015  inch  in  thickness.  If  thicker 
material,  such  as  ordinary  stove-pipe  iron,  is  used,  enough  plates  should 
be  employed  to  build  the  core  up  to  1  inch  in  thickness.  The  cross  sec- 
tion of  the  finished  core  is  1  square  inch.  The  core  weighs  about  -U 
pounds.  The  longer  strips  constitute  the  "legs"  of  the  transformer  core. 
over  which  are  slipped  the  forms  or  spools  on  which  are  wound  the  pri- 
mary and  secondary  coils.  The  shorter  strips  constitute  the  end  "yokes" 
connecting  the  "legs"  'and  forming  a  closed  core;  or  a  closed  magnetic 
circuit.  Figures  9  and  10  show  how  to  assemble  the  core  and  clamp 
the  iron  strips  in  position.  By  removing  one  end  block  and  its  clamping 
strip,  as  shown  in  figure  10,  the  coil  bobbins  or  forms  may  be  slipped 
on  over  the  "legs"  of  the  transformer  core. 


Fig.  9. 


How  to  Make  Low-Pressure  Transformers. 


17 


Fig.  10. 


It  will  be  advisable  to  carefully  remove  all  sharp  edges  from  the 
> trips  by  using  a  file,  and  to  carefully  varnish  both  sides  and  edges'  of  each 
strip  with  shellac  varnish,  allowing  the  varnish  to  thoroughly  dry  before 
beginning  the  assembling  of  the  core. 

The  ends  of  the  spools  or  bobbins  are  made  of  wood,  figure  11,  which 
are  glued  to  the  cardboard  tube  made  of  a  single  piece,  and  folded  into 
shape  as  indicated  in  figure  12.  By  cutting  partly  through  the 
cardboard  with  a  sharp  pen  knife  as  indicated  in  figure  12,  the  cardboard 
may  be  more  readily  formed  into  the  required  shape. 


f/g.14 


Fig.  11. 


Fig 


is 


How  to  Make  Low-Pressure  Transformers. 


The  two  forms  or  spools  may  be  wound  with  tape  as  indicated  in 
figure  13;  either  ordinary  electricians'  sticky  tape  may  be  used,  or  cloth 
tape  may  be  used  and  carefully  shellacked  and  allowed  to  dry  before 
winding  the  wires  on  the  spools. 

To  facilitate  winding  the  coils  on  the  spools  a  device  such  as  illustrated 
in  figure  15,  will  be  found  very  useful,  and  consists  of  a  slightly  tapering 
wooden  mandrel  shown  in  figure  14,  page  17,  having  a  j  "  diameter  hole 
lengthwise  through  its  center  to  allow  it  to  be  slipped  onto  a  \"  diameter 
shaft  of  iron  or  brass  rod,  bent  into  a  crank  at  one  end.  The  tapering 
wooden  mandrel  may  be  made  in  two  parts  as  indicated  in  figures  14  and 
15,  and  provided  with  screws,  either  ordinary  wood  screws  or  stove  bolts, 
for  clamping  the  mandrel  to  the  shaft.  The  forms  for  the  coils  may  be 
slipped  over  the  wooden  mandrel,  placed  in  position  as  indicated  in  figure 
15,  and  the  coils  readily  wound. 


How  to  Make  Low-Pressure  Transformers. 


19 


The  primary  winding  on  each  spool  consists  of  260  turns  of  No.  25 
copper  magnet  wire,  double  cotten  covered,  wound  in  two  layers.  After 
giving  the  primary  windings  two  or  three  coats  of  shellac  varnish,  the 
secondary  may  be  wound  directly  over  the  primary.  The  secondary 
consists  of  two  layers  of  No.  14,  double  cotton  covered  copper  magnet 
wire;  50  turns  per  layer.  The  primary  may  be  wound  in  two  sections 
per  spool,  bringing  out  four  terminals.  The  secondary  should  be  wound 
in  two  sections,  bringing  out  four  terminals. 

For  110  volts  60  cycles  primary,  connect  all  the  primary  sections 
together  in  series.  The  pressure  between  the  terminals  of  each  section 
of  the  secondary  will  be  about  5  volts;  or  all  connected  together  in  series 
about  20  volts. 

If  a  tap  is  brought  out  from  the  middle  of  a  secondary  section  (or 
layer)  the  pressure  of  1\  volts  per  half  section  may  be  obtained.  If 
desired  an  extra  layer  of  25  turns  may  be  wound  over  the  secondary 
to  obtain  2|  volts. 

From  10  to  15  ampers  may  be  obtained  from  the  secondary  of  this 
transformer.  Even  20  to  25  ampers  may  be  taken  for  short  intervals. 


Fig.  16. 


20  Hotr  tr>  M<ike  Low-Pressure  Transformers. 

Figure  16,  page  19.  will  serve  to  give  an  idea  of  the  appearance  of  the 
finished  transformer.  If  constructed  as  outlined  and  the  primary  connected 
in  series  as  at  PI  P  and  P2,  and  PI  and  P2  connected  across  110  volt,  60  cycle 
mains,  the  pressure  between  S  and  Si  \ 

So  and  83      f    will  be  about  5  volts 

54  and  SG 

55  and  S7 

If  S  and  82,  83  and  SG,  84  and  85  are  connected  together,  the  pressure 
between  Si  and  87  will  be  about  20  volts. 

An  important  fact  regarding  the  relation  between  the  number  of 
turns  in  the  windings  of  coils  and  the  current  in  the  coils  may  serve  as  a 
guide  in  experimenting  with  different  windings. 

If  the  number  of  turns  are  doubled,  the  current  will  be  reduced  in 
value  very  nearly  one-fourth',  assuming  the  same  frequency  and  applied 
pressure, 

For  example  in  the  transformer  last  described,  with  one  end  yoke  re- 
moved, if  110  volts  at  60  cycles  be  applied  to  one  primary  coil  of  260  turns 
about  3^  ampers  result  in  the  coil,  while  with  the  two  primary  coils  in 
,  making  a  total  of  520  turns,  with  the  same  pressure  and  frequency 
only  a  trifle  less  than  1  ampere  results. 

USING  OLD  TIN  CANS  FOR  TRANSFORMER  CORES. 

The  ordinary  so-called  "tin"  cans  that  are  now  so  extensively  employ- 
ed in  the  distribution  of  canned  goods,  are  really  made  of  thin  rolled  steel, 
coated  over  with  a  thin  layer  of  the  metal  tin.  If  these  discarded  cans 
are  placed  on  top  of  a  hot  coal  fire,  the  tin,  together  with  the  solder  used 
to  make  the  joints  tight,  may  be  melted  off,  allowing  the  ends  of  the  cans 
to  be  knocked  off.  After  the  tin  has  been  melted  off  and  the  thin  metal 
of  the  cans  kept  at  a  red  heat  for  a  few  moments,  the  cans  may  be  removed 
from  the  fire  and  allowed  to  cool  slowly.  The  slower  they  are  cooled  the 
better  the  metal  will  be  annealed  or  softened.  After  the  metal  has  become 
cold  it  may  be  cut  into  any  desired  shape  by  means  of  ordinary  tinsmith's 
shears.  After  being  properly  treated  as  outlined  above,  the  metal  will  be 
covered  with  a  thin  coating  of  oxide  that  is  very  desirable,  since  it  serves 
as  an  insulator.  The  shellac  varnish  should  be  applied  to  this  coating  of 
oxide.  Never  attempt  to  remove  the  coating  of  oxide.  The  metal  may 
be  flattened  by  hammering  gently  with  a  small  wooden  mallet,  or  a  number 
of  the  cut  pieces  may  be  laid  together,  one  on  top  of  another  and  compressed 
together  in  a  vise;  or  between  screw  clamps. 

Discarded  varnish  cans,  maple  syrup  cans,  milk  cans  and  "tin" 
pails  may  be  treated  as  suggested  and  used  for  transformer  cores. 


How  to,  M 'afye  Low-1'-.'  :•.»•••  -urc  '/',-•</ /-•N/o/vm-rx.  21 

It  may  be  noted  that  in  all  the  types  of  transformers  described, 
the  primary  and  the  secondary  are  always  wound  on  the  same  limb  of  the 
core;  or  over  one  another.  This  construction  is  much  more  efficient 
than  placing  the  primary  on  one  limb  or  section  of  the  core  and  the 
secondary  on  another  section,  as  is  sometimes  advised. 

NOTE  FOR  EXPERIMENTERS. 

It  will  be  well  to  note  that  trial  windings  may  be  wound  on  one 
of  these  transformers  at  any  time.  That  is,  one  turn  of  a  10  foot  length 
of  insulated  wire  may  be  wound  on  over  the  secondary  winding,  and  the 
terminals  of  the  10  foot  length  employed  as  "live  ends",  when  the  trans- 
former primary  is  operating.  If  the  pressure  is  not  sufficient,  wind  on 
another  turn,  and  again  test  the  pressure  between  the  terminals  of  the 
lost  wire.  Repeat  the  process  as  desired,  for  gradually  increasing  the 
useful  pressure. 

USEFUL  APPLICATIONS  OF  LOW-PRESSURE 
TRANSFORMERS. 

Many  of  the  small  transformers  made  as  specified  on  pages  4  to  9 
have  been  employed  to  ring  door  bells  in  place  of  batteries;  to  operate 
small  arc  lights  using  small  pencil  carbons;  to  operate  low  pressure  in- 
candescent lamps;  for  electro-welding;  to  charge  storage  cells,  using  an 
electrolytic  rectifier,  and  to  operate  small  direct-current  series  motors, 
either  fan  motors  or  those  on  toy  electric  railways. 

It  is  possible  to  operate  a  direct-current  series  motor  from  alter- 
nating-current mains,  because  the  reversal  of  the  alternating-current 
occurs  at  the  same  instant  iti  both  the  field  windings  and  in  the  arma- 
ture windings,  so  that  the  armature  pull,  or  the  turning  effort  always 
acts  in  the  same  direction.  The  direction  of  armature  rotation  may 
be  reversed  by  reversing  the  connections  of  the  armature  terminals  rel- 
ative to  the  field  terminals.  That  is,  to  reverse  the  direction  of  armature 
rotation,  reverse  either  the  field  or  the  armature  connections  but  not  both. 
This  rule  holds  true  for  a  series  motor  when  operated  by  cither  direct - 
current  or  alternating-current. 

TO  OPERATE  SPARK  COILS. 

Another  useful  application  is  for  operating  spark  coils  for  ga,s  or 
gasolene  engine  ignition. 


22  How  to  Make  Low-Pressure  Transformers. 

The  transformer  may  have  the  terminals  of  one  of  its  secondary 
sections  connected  with  the  primary  of  an  ordinary  jump  spark  coil, 
allowing  the  vibrator  to  operate  as  usual.  No  fixed  directions  can  be 
offered  to  goverri  this  class  of  service,  since  spark  coils  are  so  varied  in 
construction.  Judgement  must  be  exercised  as  regards  the  pressure 
to  be  applied  to  a  given  coil;  starting  with  a  low  pressure  and  gradually 
increasing  it  as  required. 

STEP-UP  TRANSFORMERS. 

As  many  questions  have  been  received  regarding  the  use  of  low- 
pressure  transformers  to  step-up  the  pressure,  a  few  words  may  be  in  order 
regarding  the  matter  in  general.  As  outlined  in  this  book,  the  designs 
are  not  such  as  to  warrant  primary  or  secondary  pressures  much  exceeding 
25%  greater  than  the  values  mentioned.  It  is  however  perfectly  per- 
missible to  apply  a  low  pressure  to  the  secondaries  of  these  transformers 
and  then  obtain  110  volts  (or  220  volts)  from  the  primaries;.  That  is 
the  transformers  may  be  used  as  step-up  transformers,  if  their  rated  pres- 
sures are  not  exceeded.  Some  have  built  8  to  16  volt  alternators  and 
used  these  transformers  to  step  the  pressure  up  to  110  volts.  In  such 
cases  what  are  called  primaries  in  this  book  become  in  reality  secondaries, 
and  vice  versa. 


Books  for  Teachers,  Students  and 
Amateurs. 

By  Prof.  F.  E.  Austin,  Box  441  Hanover,  N.  H. 

4 'Directions  for  Designing,  Making  and  Operating  High  Pres- 
sure Transformers,"  postpaid,  65cts. 

This  book  is  written  for  those  Experimenters  who  desire  to  construct 
their  own  apparatus,  and  contains  a  large  number  of  working  directions 
and  useful  hints.  It  describes  the  making  of  a  "Step-up"transformer 
giving  20,000  volts  for  Wireless  Telegraphs  and  Telephones,  and  for 
operating  tube  lamps,  X-ray  tubes,  etc.  The  book  is  well  illustrated, 
showing  special  methods  of  procedure,  fundamental  theories  and  finished 
apparatus.  It  is  plainly  written  and  the  mathematical  matter  is  treated 
in  quite  a  simple  way.  It  is  full  of  new  ideas  relating  to  methods  of  design 
and  construction. 

REVIEW  FROM  THE  WIRELESS  WORLD,  June,  1916,  London,  Eng. 
"Directions  for  Designing,  Making  and  Operating  High  Pressure 
Transformers"  by  Professor  F.  E.  Austin,  Hanover,  N.  H.r  Professor 
F. -E.Austin.  3s.net. 

This  is  an  interesting  and  clearly  written  little  book,  particularly 
valuable  to  the  serious  student  of  wireless  and  to  the  operator  who  is 
anxious  to  understand  thoroughly  the  principles  and  construction  of  the 
component  parts  of  his  installation. 

The  author  introduces  the  subject  by  referring  to  the  commercial 
demand  and  necessity  for  electric  power  at  high  pressure,  and  the  reasons 
why  alternating  current  is  the  most  useful  for  this  purpose.  A  simple 
but  very  practical  explanation  of  the  construction  of  the  transformer 
then  follows,  after  which  we  find  an  explanation  of  symbols  and  anno- 
tation, the  various  losses  in  a  transformer,  power  factor,  and  other  matters. 
The  author  next  treats  of  the  design  of  a  20,000  volt  transformer,  entering 
very  carefully  into  practical  details  of  calculation.  Following  this,  we 
have  a  chapter  entitled  "Directions  and  Data  for  Constructing  a  3-KW. 
20,000  volt  Transformer,"  the  approximate  cost  of  materials  not  being 
overlooked.  A  further  chapter  deals  with  data  applying  to  a  4,000-volt 
transformer. 

We  do  not  remember  having  previously  seen  any  small  book  dealing 
so  thoroughly  and  practically  with  the  construction  of  high  pressure 
transformers,  nor  one  in  which  the  diagrams  and  photographic  illustra- 
tions were  so  happily  chosen.  The  impression  we  have  gained  after 
reading  the  book  is  that  the  author  knows  exactly  what  he  is  talking  about 
and  how  to  express  himself. 


EXAMPLES  IN  MAGNETISM,  second  edition,  flexible  leather,  $1.10. 
From  THE  WIRELESS  WORLD,  London,  Eng.,  June,  1916. 

"Examples  in  Magnetism  for  Students  of  Physics  and  Engi- 
neering." By  F.  E.  Austin,  B.  S.,  E.  E.  Published  by  the  Author  at 
Hanover,  N.  H.  5s.  net. 

This  is  a  book  similar  in  style  to  ''Examples  in  Alternating  Currents," 
by  the  same  author,  reviewed  in  our  March  issue.  The  plates  arc  parti- 
cularly interesting  and  helpful,  as  they  show  the  lines  of  force  surrounding 
magnets  by  means  of  actual  photographs  of  iron  filings.  This  is  a  great 
improvement  on  the  old  method  of  drawing  an  imaginary  field  with  a 
few  dotted  lines,  and  should  be  much  appreciated  by  the  student. 

The  problems  and  examples  seem  carefully  chosen  and  well  worked  out. 
and  should  furnish  a  guide  to  students  who  are  beginning  to  study  elec- 
trical engineering,  and  enables  them  to  develop  the  process  of  correct 
and  logical  thinking. 

The  book  is  well  produced,  and  will  prove  valuable  to  both 
students  and  instructors. 

EXAMPLES   IN  ALTERNATING   CURRENTS,   second  edition,  flex- 
ible leather,  82.40. 

Notation — The    Pythagorean    Theorem — Trigonometrical    Functions    of    the    sum 
and  difference   of  two   Angles — Tabulation   of  Trigonometrical   Functions — Relations   of 
Trigonometrical  Functions  of  double  and  half  Angles — Expressions  involving  the  Powers  of 
Trigonometrical    Functions — Relations   of   Trigonometrical   Functions   of   three   or   more 
angles — Some   Trigonometrical   Relation  — Resultant   of    Two   Forces — Solution   of   Tri- 
angles— Rules  for  differentiating  the  Elementary  Functions  involving  a  Single  Variable — 
Differential  of   Inverse  Trigonometrical  Functions — Method  for  Finding  the  Length  of 
Curves — Integration — Definitions —   Frequency — Production   of   Electro-Motive    Force — 
average  Value  of    Sine-curve — Rate  of  change  of  Sine-curve — Alternating  Quantities-- 
How  to  Plot  the  "Curve  of  Squares"  for  a  Circle — Methods  of  finding  the  Areas  of  Cur 
Equivalent  Sine-curve — Effective  or  R.  M.  S.  Values  of  non-sine-pressures — Instantaneous 
values   of    non-sine-pressures    and   Currents — Resultant    of   Four   Pressures — Addition    of 
Sine-Pressures — Non-sine  alternating  Curves — Product    of    two    Sine-curves    having    the 
same  frequency — Product  of  two  Sine-curves  having  the  same  frequency  but  with  different 
Phase    Displacements — Inductance   of   Coils — Co-efficient    of    Inductance    of    '' 
dilation  of  the  Co-efficient  of  Inductance  of  a  Coil — Inductance  of  Transmis- 
Inductance  of   Field   Coils — Power  Factor — Inductive'  Impedances  in  Series — Two    Im- 
pedances in  Parallel — Parallel  Arrangements — Parallel  Series  Arrangements  of  In<i 
and  non-inductive   Resistances — -Fundamental  Considerations  of  Carmciu 
Condensers  in  Terms  of  their  Dimensions — Table  of  Specific;  Indi, 
]( -ctjcs — Current    in   Condensers — Effect    of   Capacity    on    Instantaneous    \ ':;. 
mum   Current    values — Capacities   of   Cm:  '• -tiding   on   their   A'rrangemei;: 

compute  Current  in  any  v  — Resonance— .Index,  and  important  tables  tor  - 

time  in  solving  problems. 

E.  &  F.  N.  SPON,  Ltd. 

57  Haymarket,  London, 

are  the  authorized  distributors  throughout  England,   Ireland,   Scotland. 
Australia  and  New  Zealand,  of  all  of  the  books  published  by  Proi'- 
F.  K.  Austin. 


IMPORTANT   NEW  BOOKS 

Ready  for  the  fall  of  1916. 

PRELIMINARY  MATHEMATICS,   flexible  leather,  $1.20 

This  is  the  most  instructive  and  valuable  book  ever  produced  to  assist 
boys  and  girls  who  are  pursuing  courses  in  Grammar  and  High  Schools, 
and  also  for  any  who  are  attempting  by  themselves  the  study  of  any  kind 
of  engineering. 

Treats  of  Algebra  and  Arithmetic,  showing  by  carefully  arranged 
worked  out  examples  how  to  solve  many  problems  in  Algebra. 

Is  really  a  complete  course  of  instruction  in  the  fundamentals  of  Mathe- 
matics, showing  methods  and  practical  applications. 

Examples  in  Battery  Engineering,  cloth,  $1.25. 

This  book  treats  of  both  primary  and  storage  cells  and  batteries 
from  the  engineering  standpoint. 

Generator  and  Motor  Examples,  in  flexible  leather,  $2.00. 

A  very  useful  and  valuable  book  for  those  desiring  a  clear  explanation 
of  the  fundamental  principle  of  direct-current  generator  and  motor  design 
and  operation.  Remit  amount  to  the  author  or  to  the  following: 

E.  <fc  F.  N.  Spon,  Ltd.,  distributors  for  England.  57  Haymarket,  London, 
England. 

Renouf  Publishing  Co.,  distributors  for  Canada.   25  McGill  College  Ave., 
Montreal,  Canada. 

p>.  Van  Nostrand  Company,  25  Park  Place,  New  York,  N.  Y. 
Putnams,  2  West  45th  St.,  New  York,  N.  Y. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
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WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
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MAY  151933 
MAY  16  1933 

23  1936 


APR 


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1940 


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IUN    3    1942 

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